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The loading tides are calculated by means of the Green’s function method based on a high-resolution regional ocean tide model, the TOPO7.0 global ocean tide model, and the Gutenberg-Bullen A Earth model. The results show that the maximal amplitude of M2 vertical displacement loading (VDL) tide in the Bohai, Yellow, and East China Seas exceeding 28 mm appears 150 km off the Zhejiang coast; the second maximum exceeding 20 mm appears in Inchon Bay; and the third maximum exceeding 14 mm is located in the northeast of the North Yellow Sea. The maximal amplitudes of S2 VDL tide at the above three locations exceed 10, 8, and 4 mm, respectively. The maximal amplitudes of the K1 and O1 VDL tides, exceeding 13 and 10 mm respectively, appear near the central and north Ryukyu Islands; the amplitudes tend to decease toward the inward areas. The phases of semidiurnal VDL tides are basically opposite to those of corresponding ocean tides. The phases of diurnal VDL tides are basically opposite to those of corresponding ocean tides in the most part of the East China Sea and the eastern part of the South Yellow Sea. This anti-phase relationship generally does not hold in the rest parts of the Bohai and Yellow Seas. The distribution patterns of self-attraction and loading (SAL) tides are very similar to those of VDL tides. The SAL tides have amplitudes about 1.2–1.7 times of the corresponding VDL tides and their phases are basically opposite to the corresponding VDL tides. The maximal amplitude of M2 SAL tide also appears off the Zhejiang coast, with a magnitude exceeding 42 mm. Bohai Sea, Yellow Sea, East China Sea, ocean tides, loading tides, self-attraction and loading tides

A dataset of drifting buoys from the Marine Environmental Data Service of Canada was analyzed to map surface circulation of the Pacific. More information of the surface circulation than that acquired before was reported in this paper, showing clear and strong western boundary currents, equatorial currents, and subtropical gyres in the North and South Pacific regions in velocity field, with a more systematic structure in the North Pacific.

The existing estimates of the volume transport from the Pacific Ocean to the South China Sea are summarized, showing an annual mean westward transport, with the Taiwan Strait outflow subtracted, of 3.5±2.0 Sv (1 Sv=106 m3 s−1). Results of a global ocean circulation model show an annual mean transport of 3.9 Sv from the Pacific to the Indian Ocean through the South China Sea. The boreal winter transport is larger and exhibits a South China Sea branch of the Pacific-to-Indian Ocean throughflow, which originates from the western Philippine Sea toward the Indonesian Seas through the South China Sea, as well as through the Karimata and Mindoro Straits. The southwestward current near the continental slope of the northern South China Sea is shown to be a combination of this branch and the interior circulation gyre. This winter branch can be confirmed by trajectories of satellite-tracked drifters, which clearly show a flow from the Luzon Strait to the Karimata Strait in winter. In summer, the flow in the Karimata Strait is reversed. Numerical model results indicate that the Pacific water can enter the South China Sea and exit toward the Sulu Sea, but no observational evidence is available. The roles of the throughflow branch in the circulation, water properties and air-sea exchange of the South China Sea, and in enhancing and regulating the volume transport and reducing the heat transport of the Indonesian Throughflow, are discussed.

A POM based three-dimension baroclinic prognostic model in σ-coordinate was established to simulate the eddies in the East China Seas wintertime circulation, considering the topography, inflow and outflow on the open boundary, Changjiang runoff, heat, flux, and wind stress on the sea surface. The model results showed that three branches separate from the Kuroshio flow toward the interior of the Yellow Sea, and form three eddies respectively. The middle eddy is centered at 124°37′E, 37°00′N, the southern eddy is centered at 124°00′E, 35°30′N. The large cyclonic eddy centered at 125°06′E, 30°30′N and located southwest of Cheju Island is a closed structure formed by the northeastward flowing Taiwan Warm Current, northwestward flowing Yellow Sea Warm Current and southward flowing coastal current. The Kuroshio intrusion engenders an eddy west of Kyushu Island of Japan. The branching of the Kuroshio is the direct dynamic cause of the formation of this large eddy. Moreover, both the topographic influence and the northward wind prevailing in winter affect the eddy's formation obviously.

A fine-grid model (1/6°) covering the South China Sea (SCS), East China Sea and Japan/East Sea, which is embedded into a coarse-grid (3°) global model, was established to study the SCS circulation. In the present paper, we report the model-produced monthly and annual mean transport stream functions and sea surface heights(SSH) and their anomalies of the SCS. Comparison to the TOPEX/Poseidon data shows that the model-produced monthly sea surface height anomalies (SSHA) are in good agreement with altimeter measurements. Based on the results, the circulation of the SCS, especially the upper layer circulation, is discussed. In the surface layer, the western Philippine Sea water intrudes into the SCS through the Luzon Strait in autumn, winter and spring, but not in summer. However, as far as the whole water column is concerned, the water intrudes into the SCS through the Luzon Strait all the year round. This indicates that in summer the water still intrudes into the SCS in the subsurface and intermediate layers. The area near the northern continental slope of the SCS is dominated by a cyclonic circulation all the year round. The SCS Southern Anticyclonic Gyre, SE Vietnam Off-Shore Current in summertime and SCS Southern Cyclonic Gyre in wintertime are reproduced reasonably. The difference between the monthly averaged SSH and SSHA is significant, indicating the importance of the mean SSH in the SCS circulation.

The monthly and annual mean freshwater, heat and salt transport through the open boundaries of the South and East China Seas derived from a variable-grid global ocean circulation model is reported. The model has 1/6degrees resolution for the seas adjacent to China and 30 resolution for the global ocean. The model results are in fairly good agreement with the existing estimates based on measurements. The computation shows that the flows passing through the South China Sea contribute volume, heat and salt transport of 5.3 Sv, 0.57 PW and 184 Ggs(-1), respectively (about 1/4) to the Indonesian Throughflow, indicating that the South China Sea is an important pathway of the Pacific to Indian Ocean throughflow. The volume, heat and salt transport of the Kuroshio in the East China Sea is 25.6 Sv, 2.32 PW and 894 Ggs(-1), respectively. Less than 1/4 of this transport passes through the passage between Iriomote and Okinawa. The calculation of heat balance indicates that the South China Sea absorbs net heat flux from the sun and atmosphere with a rate of 0.08 PW, while the atmosphere gains net heat flux from the Baohai, Yellow and East China Seas with a rate of 0.05 PW.

In this part, Levitus' climatological temperature and salinity are incorporated in the model developed in Part I. Diagnostic and prognostic experiment on the thermohaline circulation were conducted. The smooth Levitus' data do not include any information on the South China Sea Warm Current (SCSWC), so it is not in the model-produced diagnostic thermohaline circulation. Although the SCSWC does not appear in the wind-driven circulation in the barotropic case, it appears in the prognostic wind-driven circulation in the baroclinic case. This implies that the differing circulation patterns between barotropic case and baroclinic case are due to the stratification. The prognostic thermohaline circulation with wind stress and inflow/outflow transports at open boundaries are also discussed. Coupling of density and dynamic forces makes the circulation pattern more complicated. Even though the stratification is not always a direct cause of the formation of the SCSWC, it is at least an indirect cause.

Global ocean tides data were derived from Geosat altimeter data by means of the Quasi-Harmonic Constituent Method (QHCM). Tidal solutions with resolution of 1°/3 in longitude and latitude were obtained for constituentsM 2,S 2,O 1,K 1,M 4 andMS 4. The means sea heights above the reference ellipsoid were also obtained consequently. The obtained tidal constants were compared with those from deepsea and island tide gauge data. The rms differences between the harmonic constants derived from Geosat altimetry and deep-sea tide gauges forM 2,S 2,O 1 andK 1 ranged from 1.4 cm to 2.6 cm, although the GM altimeter data have significant errors due to instrument malfunction and other reasons.M 2 tide obtained was the most accurate one among all the tides. Comparison also showed that island tidal constants cannot represent well the tidal distribution in the ocean near the island, because of the significant local effect on tides.

This numerical study of the Bohai Sea wintertime circulation by means of a two dimensional barotropic model with resolution of 1/24° in longitude and latitude showed that the Bohai Sea wintertime circulation is dominated by local monsoon winds. The major current components include the Bohai Warm Current, the North Shandong Coastal Current, and the Liaodong Gyre. The Bohai Warm Current originates from the Yellow Sea Warm Current at the northern part of Bohai Strait, meanders westwards and finally enters the northern part of Bohai Bay. The North Shandong Coastal Current flows along the southwest shore of Bohai Bay and Laizhou Bay and exits from the Bohai Sea through the south Bohai Strait. The anticyclonic Liaodong Gyre is located in the north of Liaodong Bay. A pair of eddies and the small scale Jinzhou Gyre are found between the Bohai Warm Current and the Liaodong Gyre. The computed volume transport for both the Bohai Warm Current and North Shandong Coastal Current is about 0.03 Sv (1 Sv=1×106 m3/s). The numerical experiments showed that the combined effect of local monsoon winds and bottom topography dominate the formation of the circulation pattern. The Coriolis force and the wind stress curl are of certain importance. The beta effect, the momentum advection and the open boundary condition have little influence on the circulation pattern.

The layered model in Part I was used to simulate the internal tide in a stratified, two layer, and rectangular sea area with step-like topography. The internal tide current velocities of the upper and lower layers and the interfacial elevations were computed and the effect of the upper layer water depth and density difference were studied. Numerical experiments verified that the model can correctly simulate internal tides. The model was also applied to the northwestern part of the South China Sea to simulate the internal tides there with real topography. The distributions of internal tide amplitude in interfaces were delineated.

This paper deals with the derivation of a series of seemingly simple but ignored relations, and presents several identities for fluids never obtained before (relations of integrals over different sets of independent variables and connected by an invertible mapping). These identities are based on mass conservation and a mathematical transform with no restriction on dynamics. They are, however, crucial to some fundamental concepts and the interpretation of results from dynamics. The identity for momentum is of most importance and, when averaged over time, yields a relationship between the spatially integrated and time-averaged Lagrangian momentum and the spatially integrated and time-averaged Eulerian momentum. For a constant density fluid, the averaged identity reduces to a relation between the integrated mean displacement of the particles and the integrated mean Eulerian velocity. For an exactly oscillatory flow in an Eulerian description this identity yields a zero integrated mean displacement of particles. In the case of a progressive surface gravity wave, which is periodic but not exactly oscillatory in an Eulerian description such that there are no particles above the trough during part of the period, the mean momentum identity ensures that the integrated mean Eulerian momentum is equal to the integrated mean momentum of the particles. Therefore, there is essentially no superiority as to which description gives a better estimate of the total momentum or total transport at the same order of approximation. The widely used relation, that the Lagrangian velocity equals the Eulerian velocity plus the Stokes velocity, is not based on a 1 to 1 invertible mapping and is therefore ambiguous. This relation is not valid where there is a discontinuity, particularly above the wave trough. It can therefore give an incorrect result on the Lagrangian velocity. The Generalized Lagrangian Mean (GLM) theory uses a mapping between the mean positions of particles and the particles themselves and apparently avoids the non-invertibility. However, this mapping is actually not invertible in general because different particles may have the same mean position.

The stability, accuracy, and dispersion of a semi-implicit finite difference scheme for the numerical solution of external mode were carefully analyzed in this study. The stability analysis was implemented with the von Neumann method and proved that the scheme is unconditionally stable. Study of their accuracy showed that the finite difference equations were consistent with the differential equations with second-order accuracy. The Eulerian-Lagrangian discretization of the convective terms was also discussed. The existence of dispersion was proved to be unfavorable for the achievement of the real solution.

In this numerical model for simulating the Kuroshio intrusion into the East and South China Seas, vertically averaged marine hydrodynamic equations governing ocean currents and long-period waves are approximated by a set of two-time-level semi-implicit fimite difference equations. The major terms including the local acoeleration, sea-surface slope, Coriolis force and the bottom friction are approximated with the Crank-Nicholson scheme, which is of second order accuracy. The advection terms are approximated with the Leith scheme. The difference equations are split into two sets of alternating direction implicit equations, each of which has a tridiagonal matrix and can be easily solved.

A time-correlated random field describing the general flow is defined. A time-correlated functional equation governing the evolution of its characteristic functional is derived.

A so called sine-sigma vertical coordinate transformation is proposed. A vertical implicit scheme is derived by using cubic-spline representation of vertical current profiles. The derived 3-D numerical model has been applied to simulate the water level field and the vertical structures of wind-induced currents in an enclosed rectangular region, and the tides in the Bohai Sea. The model is believed to be satisfactory after comparing its results with an analytical solution and observed data from tidal stations.